Do smells/odors ever truly disappear or do they just dissipate to the point that eventually we cannot smell the original odor and each one is permanently adding however miniscule an amount to an overall smell on the planet?
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The answer to this question really depends on your detection threshold, ie how little of something needs to be present for you to say it’s still there.
Smells work because small, light weight molecules evaporate and become airborne, before entering into our nose. While in our nose, these molecules bind to one (one more) smell receptor nerves in our sinus cavity. This works like a infant’s toy of sorting the square blocks into the square hole, any molecule with a particular shape can activate a specific smell receptor. Often molecules have multiple recognizable shapes, and so activate multiple receptors. The smell we perceive is based on the different kinds of receptors that were activated, and how many of each. Once the molecule binds to the smell receptor, it then breaks free and is exhaled into the air again.
The part that’s important to your question is, unlike food, we don’t destroy the smell molecules, we just briefly bind them to our receptors and then exhale them again. When we stop being able to smell something, it’s for a psychological reason that we became blind to this input, not because we physically can’t detect the molecule anymore. All smell molecules are dissipating into the atmosphere, where they remain (mostly). So, the answer to the question “how long can I smell my fart” ultimately depends on how sensitive to your fart smell you are, because it’s still present in the atmosphere, just at such a low concentration that you can’t smell it anymore
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